High‐performance SIMD modular arithmetic for polynomial evaluation. (25th May 2021)

• Record Type: Journal Article
• Authors: Fortin, Pierre; Fleury, Ambroise; Lemaire, François; Monagan, Michael
• Is Part Of: Concurrency and computation. Volume 33:Number 16(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-05-25
• Subjects: instruction‐level parallelism -- modular arithmetic -- operational intensity -- polynomial evaluation -- SIMD; Parallel processing (Electronic computers) -- Periodicals; Parallel computers -- Periodicals; 004.35
• DOI: 10.1002/cpe.6270
• Languages: English
• ISSNs: 1532-0626

Abstract

Summary: Two essential problems in computer algebra, namely polynomial factorization and polynomial greatest common divisor computation, can be efficiently solved thanks to multiple polynomial evaluations in two variables using modular arithmetic. In this article, we focus on the efficient computation of such polynomial evaluations on one single CPU core. We first show how to leverage SIMD (single instruction, multiple data) computing for modular arithmetic on AVX2 and AVX‐512 units, using both intrinsics and OpenMP compiler directives. Then we manage to increase the operational intensity and to exploit instruction‐level parallelism in order to increase the compute efficiency of these polynomial evaluations. All this results in the end to performance gains up to about 5x on AVX2 and 10x on AVX‐512.